endogenous networks in investment syndication

Electronic copy available at: http://ssrn.com/abstract=1885299

Forthcoming in Journal of Corporate Finance

Endogenous Networks in Investment Syndication*

Lanfang Wang1 and Susheng Wang2

January 2012

Abstract: As an effective investment strategy, investors often invest jointly in a company by

forming a syndicate. The unique feature of this paper is that it endogenizes the formation of

an investment syndicate. We provide a theory on the endogenous formation of networks in

investment syndication and analyze how several key factors such as risk aversion, productiv-

ity, risk and cost affect incentive and syndicated investment. We also apply the theory to

venture capital investment and identify empirical evidence in support of it.

Keywords: investment syndication, endogenous network, investment risk, risk aversion,

project productivity

JEL Classification: G30

* We gratefully acknowledge helpful comments and suggestions from an anonymous referee, which led to a substantial improvement of the paper.

1 Assistant Professor at Institute of Accounting and Finance, Shanghai University of Finance and Economics.

Email: [email protected].

2 Professor at Hong Kong University of Science and Technology. Email: [email protected].

Electronic copy available at: http://ssrn.com/abstract=1885299

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1. Introduction

Risk-averse investors demand large compensation for investing in highly risky projects.

One effective strategy for investors to deal with risks is to form a group to invest jointly in a

firm. This way a number of investors can share the risks, especially when investing in a

highly risky firm. This group of investors is referred to as an investment syndicate and the

company being invested in is referred to as a portfolio company. An investment syndicate is

a form of interfirm alliances in which two or more venture capital firms or investment banks

(investors) co-invest in a portfolio company and share a payoff (Wright and Lockett, 2003).

Investment syndicates are very popular in reality. For example, Wright and Lockett (2003)

reported that 63.6% of U.S. and 29.5% of European venture capital (VC) investments were

syndicated in 2000. Brander et al. (2002) found that 60% of Canadian VC investments in

1997 involved more than one VC investor. Lerner (1994) suggested that syndication is com-

monplace even in first-round investments. In practice, an investment syndicate is typically

led by one of the investors, who actively invites other investors to join in and coordinates

investment deals between the company and the investors. This lead investor typically makes

the largest investment among the group and is involved throughout the whole investment

phase.

In the beginning, the entrepreneur (EN) of the portfolio company initiates an invest-

ment syndicate by inviting and appointing a lead investor. When deciding on whom to ap-

point as the lead investor, the EN must take into account two major factors: (1) the lead

investor’s ability in organizing a syndicate to satisfy the needs of the company; and (2) the

bargaining power of this syndicate for a share of company profits. One crucial determinant of

the lead investor’s ability to organize a syndicate is her business connections, which deter-

mines her ability in inviting suitable investors to join her syndicate. Such personal business

connections are known as the lead investor’s network capital. A well organized syndicate can

provide the necessary funding for the company. At the same time it is also in a good position

to bargain for a large share of company profits. For example, Hochberg et al. (2010) argued

for the value of networks in restricting the entry of outside venture capitalists (VCs), thus

improving the incumbents’ bargaining power with the EN. Hence, when choosing a suitable

lead investor, the EN needs to strike a balance between a syndicate’s ability in providing

funding to satisfy the company’s needs and its potential to bargain for company profits. For

this reason, an equilibrium theory should be developed on the level of the lead investor’s

network capital or more generally on the composition of an investment syndicate in equilib-

rium.

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Although syndication is very important in venture capital, little is known about the mo-

tives of syndication. Lerner (1994) pointed out that “Syndication has been little scrutinized in

the corporate finance literature. The reason may lie in the difficulty of analyzing syndication

patterns empirically and the complexity of motives behind syndication.” More recently,

Brander et al. (2002) claimed that “Aside from Lerner (1994), we are unaware of any pub-

lished academic papers in which the rationale for VC syndication is the central focus, al-

though some of the existing literature on VC finance does bear on the syndication question”.

In this study, we provide a theory on the endogenous formation of an investment syndicate.

The theoretical model has three stages. In the first stage, the EN of the portfolio company

selects a lead investor. In the second stage, the lead investor coordinates the formation of a

syndicate. In the third stage, the EN and the syndicate or the lead investor bargain for output

shares. Most of the existing studies have focused on the second stage. Our analysis shows the

impact of network endogeneity. In particular, we show opposite effects of productivity on

effort if a network is treated as exogenous instead of endogenous.

This study is related to two streams of literature. The first stream is on investment syn-

dication. Existing studies on investment syndication have focused on two questions: what is

the rationale behind investment syndication and how are investment syndicates formed?

There are many theoretical studies on the rationale behind syndication. In theoretical studies,

Wilson (1968), Sah and Stiglitz (1986) and Pichler and Wilhelm (2001) suggested that syndi-

cation is an efficient way to share risks among partners and gather additional information

about a startup’s value and can also be a way of colluding tacitly. Admati and Pleiderer (1994)

provided an implicit rationale for syndication based on information asymmetry between VCs

and the EN. They suggested that the only optimal financial contract that can mitigate overin-

vestment and other agency problems is a fixed-fraction contract. This is when the VCs re-

ceive a fixed fraction of the project’s payoff and finance the same fraction of future invest-

ments. Their theoretical model implies that the VCs’ syndication decision in later rounds

would ensure the optimality of a financial contract. Casamatta and Haritchabalet (2007)

suggested that VC syndication improves the screening process of VCs and prevents competi-

tion among investors after investment opportunities are disclosed. They also highlighted the

importance of experience to the formation and efficiency of investment syndicates, which

suggests that experienced VCs should syndicate with experienced VCs. Huang and Xu (2003)

provided a contractual foundation that solves a class of commitment problems in R&D fi-

nancing and argued that syndicated VC financing can be deployed as a commitment device to

terminate bad projects promptly. Fluck et al. (2006) provided an explanation to the popular

co-existing phenomena of staged financing and syndication in VC investments. They found

that ex ante commitment to syndicate investments in later stages protects the EN from po-

https://www.researchgate.net/publication/241037861_Venture_Capital_Contracting_Staged_Financing_and_Syndication_of_Later-stage_Investments?el=1_x_8&enrichId=rgreq-be5c315a-d93c-45c5-9f0c-165fd0d8be91&enrichSource=Y292ZXJQYWdlOzIyODI5NDU5NztBUzoxMDMyMTM3NzY3NjkwNDBAMTQwMTYxOTQ5MDg3OQ==

https://www.researchgate.net/publication/4991921_Venture-Capital_Syndication_Improved_Venture_Selection_vs_The_Value-Added_Hypothesis?el=1_x_8&enrichId=rgreq-be5c315a-d93c-45c5-9f0c-165fd0d8be91&enrichSource=Y292ZXJQYWdlOzIyODI5NDU5NztBUzoxMDMyMTM3NzY3NjkwNDBAMTQwMTYxOTQ5MDg3OQ==

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tential hold-up problems arising from staged financing. Dorobantu (2006) suggested that a

VC can use syndication in the second or a later financing round as a signaling device to

credibly communicate private information about her project-selection ability to potential

investors in a follow-on round.

The most related empirical works on the rationale of investment syndication are those of

Brander et al. (2002) and Ozdemir (2006). Brander et al. (2002) examined two conjectures:

the venture selection and value-added hypotheses. Using Canadian VC investment data, they

found that syndicated VC investments have higher returns, which supports the value-added

interpretation. A similar result was found by Cumming and Walz (2010). Ozdemir (2006)

discussed “how social structure and a VC firm’s position within it affect the propensity of

syndication.” Ozdemir confirmed that “uncertainty and risk associated with investing in a

particular target company increase the likelihood of syndication.” De Clercq and Dimov

(2004) investigated the realized investment strategies of 200 U.S.-based VCs over a twelve-

year period. Their findings suggested that syndication is a mechanism for VCs to share com-

plementary knowledge and financial risks among syndicate partners.

Unlike the rationale behind investment syndication, there are few theoretical studies on

the formation of investment syndicates. To our knowledge, the only related studies to our

work are those of Cestone et al. (2007) and Tykvová (2007). Cestone et al. (2007) focused on

contract design to induce VCs to truthfully disclose investment opportunities. Their findings

suggest that more experienced lead VCs should select more experienced partners. This con-

clusion is consistent with the implications of the theoretical work of Casamatta and Haritch-

abalet (2007) and is supported by the empirical works of Lerner (1994) and Du (2009). In

contrast, Tykvová (2007) showed in a complete information setting that VCs may choose to

syndicate with less experienced partners if the latter are willing to accept comparably worse

payoffs after taking into account the benefits of reputation building and the transfer of know-

how among partners.

The second stream of literature related to this study consists of recent studies on the ap-

plication of network theory in finance, especially VC investments. Network structure is

known to be important in determining the outcome of many important social and economic

relations.3 In finance, network theory is mainly applied to financial stability and contagion.

3 Examples of the effects of social networks on economic activity are abundant, including their effects on

transmitting information about job availability, new products, technologies and political opinions. They also

serve as channels for informal insurance and risk sharing. The network structure influences patterns of decisions

regarding education, career, hobbies, criminal activity and even participation in micro-finance. Durlauf (2004)

https://www.researchgate.net/publication/45133479_Private_Equity_Returns_and_Disclosure_Around_the_World?el=1_x_8&enrichId=rgreq-be5c315a-d93c-45c5-9f0c-165fd0d8be91&enrichSource=Y292ZXJQYWdlOzIyODI5NDU5NztBUzoxMDMyMTM3NzY3NjkwNDBAMTQwMTYxOTQ5MDg3OQ==



https://www.researchgate.net/publication/222421866_Who_Chooses_Whom_Syndication_Skills_and_Reputation?el=1_x_8&enrichId=rgreq-be5c315a-d93c-45c5-9f0c-165fd0d8be91&enrichSource=Y292ZXJQYWdlOzIyODI5NDU5NztBUzoxMDMyMTM3NzY3NjkwNDBAMTQwMTYxOTQ5MDg3OQ==

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Freixas et al. (2000), Leitner (2005), Dasgupta (2004) and Cummins et al. (2002) showed

that the existence of more network connections among banks may reduce the risk of conta-

gion. Eisenberg and Noe (2001), Afonso and Shin (2007) and Gai and Kapadia (2007) used

the techniques developed in mathematics and physics to study contagion. Lagunoff and

Schreft (2001) and Cifuentes et al. (2005) studied the impact of indirect linkages on conta-

gion. Babus (2009), Allen and Gale (2000) and Castiglionesi and Navarro (2008) studied the

issue of network formation among banks. Also, Babus’ (2009) theoretical study on the risk of

contagion among banks suggested endogenous network formation among banks. She

showed that contagion does not occur in equilibrium.

In empirical studies, Ozdemir (2006) showed that “those VC firms deeply embedded in

the VC industry syndication and social networks are more likely to initiate syndicates, al-

though the more experienced VC firms prefer going solo.” Hochberg et al. (2007) investi-

gated the effect of networks on VC investments. They looked at VCs who are connected

through a network of syndicated investments. They found that better-networked VCs experi-

ence significantly better fund performance, as measured by the proportion of investments

that are successfully exited through IPOs and sales to other companies. Hochberg et al.

(2010) further showed that VC syndication presents a potential barrier to entry for new VCs,

and incumbents appear to have benefited from this reduced entry because they show the

willingness to accept lower compensation for their deals. Hochberg et al.’s (2007, 2010)

works agrees with the earlier work of Seppä and Jääskeläinen (2003), who explored 54,700

VC investments in 10,057 portfolio companies by 100 of the largest private U.S. VCs during

1986–2000. Sorenson and Stuart (2001) explored how interfirm networks in the U.S. VC

market affect spatial patterns of exchange. Empirical evidence suggests that social networks

in the VC market—built up through the extensive use of syndicated investments—transfer

information across boundaries and therefore expand the spatial radius of exchange.

Sorenson and Stuart (2008) proposed a theory to explain the formation of distant ties in VC

investment networks and suggested that VCs form relations with distant partners when they

participate in two types of settings: unusually faddish ones and those with limited risks to

participants.

This paper examines a different aspect of the formation of investment syndicates. Previ-

ous theoretical and empirical studies have emphasized relational ties among investors but

reviewed theoretical models on neighborhood effects. Allen and Babus (2009) reviewed the application of net-

work theory in finance. Jackson (2005, 2010) gave a survey of theoretical works on network formation and

provided an overview of social networks in economic applications.

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ignored the role of the EN. In other words, they have focused on how the lead investor

chooses syndication partners, with the EN playing no role in the process. We, however, take

into account the role of the EN in the formation of the investment syndicate. We propose a

theoretical model to explain how the syndicate is determined through a process involving

choices and bargaining between the EN and the syndicate and among the syndicate members.

In our theoretical model, the syndication process involves three stages: the EN first chooses

the lead investor; then the lead investor chooses syndication partners; and finally the EN and

the syndicate bargain to determine their output shares. The first and final stages have so far

been ignored in the existing literature on the formation of investment syndicates. Our three-

stage syndication process endogenously determines the lead investor’s network capital in

equilibrium.

This paper contributes to the literature on the networks of investment syndicates. Our

model suggests that when choosing the lead investor, the EN will take into account the lead

investor’s network capability as a key factor. This is quite consistent with existing empirical

evidence. For example, Gulati (1999) found that accumulated network resources (or what we

refer to as network capital in this paper) arising from the history of participation in the net-

work of alliances are influential in a firm’s decision to join new alliances. More direct evi-

dence came from Smith (2001), who found that the factors the EN considers when evaluating

VCs include network capital, such as “co-investing with other investors”, “interfacing with

the investor group” and “obtaining alternate sources of financing.” A lead investor’s network

capital affects her ability to organize a sizable syndicate, which is proven to be valuable to

project efficiency (Brander et al., 2002). We conclude that the tradeoff between syndicated

funding and profit sharing determines the optimal choice of the EN, by which the lead inves-

tor’s network capital is endogenously determined in the process. Endogenously determined

networks can be found in the existing studies on financial networks. For example, Babus

(2009) found that a financial network of banks emerges endogenously. In equilibrium, with

endogenous networks, the degree of systemic risk is significantly reduced. Further, in certain

equilibria, contagion does not occur.

Our theoretical model shows that the determinants of the syndicate size or the lead in-

vestor’s network capital include the investors’ risk aversion, project productivity and inves-

tors’ output share. We further provide empirical evidence to support our theoretical findings

using 40,395 identified domestic VC investment rounds made in 15,264 portfolio companies

by U.S. VCs during 1985–2005. After controlling for the type of lead VC firm (lead VC type)

and the fixed effects of funding year, industry and round sequence, we found that investment

risk and portfolio company quality had a significant positive effect on the syndicate size. This

empirical finding is consistent with our theoretical results.

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This paper is organized as follows. In Section 2, we set up the model. In Section 3, we

solve for the equilibrium solution and provide a theoretical analysis of our solution. In Sec-

tion 4, we apply our theory to VC investments and present an empirical analysis using data

from the U.S. VC industry. We conclude in Section 5 with a summary of our main results and

remarks. The derivations are given in the Appendix.

2. The Model

In this section, we develop a theory on the formation of an investment syndicate supply-

ing funds to a target company.

Consider an EN who seeks investment from investors for a project. Funding is provided

through a syndicate. The syndicate is organized by a lead investor, who is invited and ap-

pointed by the EN. The syndicate is defined by a vector 1( , , , ),nn a a where n is the num-

ber of investors in the syndicate and is called the lead investor’s network capital, and ia is a

measure of the risk aversion of investor i in the syndicate. This n is endogenous. For the

investors, a larger n implies more investors to share risk and increases the bargaining power

of the syndicate for a share of output; for the EN, a larger n means more funding but re-

duces the EN’s bargaining power. An optimal n will be chosen by the EN when she selects

the lead investor.

The EN is risk neutral, and the investors are risk averse. Each investor has utility func-

tion:

11( ) .1

ii

i

u x x a

a-=

- (1)

Output is determined jointly by investment from investors and effort from the EN. The EN

has an incentive problem since her effort a is unverifiable. Specifically, output ex ante is a

lottery x defined by

( )( ), ( ); 0,1 ( ) ,x x I p a p aº -

where I is the total investment from the investors, ( )x I is the output ex post when the

project is successful, ( )p a is the probability of success, and both ( )x I and ( )p a are as-

sumed to be increasing functions. We assume ( ) ( )p a x I I* * *> in equilibrium ( , ),a I* *

implying a profitable project.

The EN bargains with the lead investor over how to divide the output after it is pro-

duced. Let ( )nl be the output share for the syndicate. Hence, ( )nl represents the bargain-

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ing power of the lead investor. We assume that ( )nl is increasing in ,n meaning that the

larger the syndicate, the more bargaining power the lead investor has.

We take the same incomplete contract approach as Hart and Moore (1990) did. In our

model setting, there is no contract ex ante at 0t = and the two parties, the EN and the syn-

dicate (SN), bargain for output shares ex post at 1.t = However, the equilibrium solution is

implementable by a complete contract ex ante. If n* is the equilibrium solution, the com-

plete contract is an upfront equity-sharing agreement that gives an equity share of ( )nl * to

the syndicate and an equity share of 1 ( )nl *- to the EN. Our model setting ensures our

solution to be bargaining-proof or renegotiation-proof.

We solve the problem backwards in three steps as indicated by the following figure.

0 1

Investors jointly provideEN applies effort

Ia

Bargain for output, for SN, 1 for ENl l-EN chooses n

Step 1: The EN’s Effort

After output is produced, the two parties bargain for a share. We assume that when bar-

gaining for a share of output, the lead investor representing the syndicate behaves as a risk-

neutral agent. This is symmetric to the setting on the EN’s side, where the risk-neutral EN

also represents a group of agents in reality, including managers, entrepreneurs and the

original owners (insiders) of the firm. Only when each investor considers her own invest-

ment does she behave as a risk-averse agent. We use the Nash bargaining solution to define

their output shares. If no agreement is made, both parties get nothing; if there is an agree-

ment, they share output .x The Nash bargaining solution implies the following ex post pay-

offs for the EN and the syndicate, respectively,

[ ]1 ( ) , ( ) ,EN SNn x n xl lP = - P =

where the subscript SN stands for the syndicate, random output x takes either ( )x I or 0,

and ( )nl represents the lead investor’s bargaining power, which is assumed to be increasing

in .n With private cost ( )c a and risk neutrality, the EN’s ex ante payoff is4

[ ]1 ( ) ( ) ( ) ( ),ENU n p a x I c al= - -

4 We can also assume that the EN is risk averse, which does not add much complexity to our analysis nor

change our conclusions.

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where ( )c a is the EN’s private cost of effort. Then, the EN chooses a according to the fol-

lowing first-order condition (FOC):

[ ]1 ( ) ( ) ( ) ( ).n p a x I c al ¢ ¢- = (2)

By assuming concave ( )p a and convex ( ),c a the second-order condition (SOC) for the

choice of a is satisfied.

Step 2: The Investors’ Investment

Consistent with reality, assume that the expected return is the same among all the inves-

tors in a syndicate. This means that each investor’s income from investment is proportional

to her investment. That is, investor i with investment iI receives a share /iI I from the

syndicate’s total income ( ) .n xl With the coordination of the lead investor, the investors

form a cooperative group. Suppose that the total investment I is to be determined by social

welfare maximization in the syndicate. Then, assuming (0) 0,iu = the syndicate’s investment

decision is determined by the following problem:

( ){ } 1

max ( ) ( ) .i

ni

SN i j ijI i jj

IU p a u n x I II

l=

ì üé ùï ïï ïê úº -í ýê úï ïê úï ïë ûî þå åå

This problem implies the total investment .I That is, it is not the lead investor who decides

;I instead, it is the syndicate that determines this I together. Based on the existing litera-

ture, we assume homogeneity among the investors in a syndicate; specifically, we assume

that all the investors in a syndicate have the same risk aversion .a Hence, we must have

/iI I n= for all i in equilibrium. Then, the FOC for the above problem is (see the Appendix

for the derivations):

1( ) ( ) ( )1 ( ) .

( )n x I x Ip a nn x I

al - ¢é ùê ú=ê úë û

(3)

This equation determines the optimal funding ˆ( , ).I a n That is, the investment is affected by

the EN’s incentive and the lead investor’s network capital.

Our assumption of homogenous investors is well justified by the literature. Casamatta

and Haritchabalet (2007) studied the rationale behind syndication. They indicated that

syndication can improve the screening process (gather information) and prevent competition

among investors. They highlighted the importance of experience to the formation and effi-

ciency of a syndicate and suggested that experienced VCs syndicate exclusively with experi-

enced partners because they possess good assessment skills. Cestone, Lerner, and White

(2007) studied the formation of VC syndicates. They also found that more experienced VCs

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select more experienced partners. Du (2009) examined VCs’ preferences for syndication

partners in an empirical study. She found that VCs are less likely to syndicate with partners

who are different from themselves.

Step 3: The EN’s Choice of Network Capital

The EN selects a lead investor with a certain network capital .n Given equations (2) and

(3), the EN’s problem is

[ ]

[ ], ,

1

1

2

max 1 ( ) ( ) ( ) ( )

s t : 1 ( ) ( ) ( ) ( ),

( ) ( ) ( ): ( ) 1.( )

n a In p a x I c a

IC n p a x I c a

n x I x IIC p a nn x I

a

l

l

l -

- -

¢ ¢. . - =

é ù ¢ê ú =ê úë û

(4)

Notice that we do not include individual rationality (IR) conditions in the problem, which

can be expressed as

[ ] ( )1

1 ( ) ( ) ( ) ( ) 0, ( ) ( ) 0.n

ii j ij

i jj

In p a x I c a p a u n x I II

l l=

ì üé ùï ïï ïê ú- - > - >í ýê úï ïê úï ïë ûî þå åå

We have no need for the IR conditions in problem (4) since we have implicitly allowed the

bargaining process to include a monetary transfer between the two parties to ensure both IR

conditions are satisfied for the EN and the syndicate. It turns out that such a transfer is

unnecessary in our model since for the set of functions we choose later in (5), the solution of

(4) automatically satisfies the two IR conditions.

To gather a group of investors to satisfy a company’s needs for funding, the lead investor

must have many network connections in the investor community. On the one hand, a well-

connected investor is able to gather a proper and sufficiently large group of investors to

provide sufficient funding and to spread risks among the investors. On the other hand, such

a well-connected lead investor has more bargaining power against the portfolio company.

Through Nash bargaining, a well-connected investor obtains a large income share from a

deal, which reduces the EN’s incentive to work. Hence, the EN needs to balance between

these two factors when she appoints a lead investor. The optimal network capacity of this

lead investor is the key in our model.

Most existing theoretical studies on investment syndication have focused on how a lead

investor chooses partners but ignored the role of the EN. Our model lets the EN choose a

lead investor with a certain network capital. This is consistent with the study by Smith

(2001), whose survey data suggests that companies in need of investment actively choose

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investors. He found a number of network factors to be important in this choice, including

“co-investing with other venture capitalists,” “interfacing with the investor group” and “ob-

taining alternate sources of financing.”

Theoretical and empirical studies have suggested that both the EN and the lead investor

are important to the project. In existing theoretical studies, either the EN or the investors

have been assumed to be the principal in their relationship. For example, in a study by Ad-

mati and Pfleiderer (1994), the EN determines the initial financing agreement in order to

maximize the net surplus of the project, while in another study by Amit et al. (1990) the VCs

determine the manager’s profit share in order to maximize their own profits. We assume that

the EN chooses a lead investor to initiate the syndication process, which is quite consistent

with the empirical evidence in the survey by Smith (2001). Smith (2001) indicated that

around 71% of ENs in his sample had a choice on which VCs should be allowed to invest in

their companies.

3. Theoretical Analysis

3.1. The Cooperative Investment Solution

To analyze the solution, we must use parametric functions. Parametric functions allow a

few parameters to represent the key aspects of the issue at hand. We choose the following

parametric functions:5

11( ) , ( ) , ( ) , ( ) , ( ) ,1iu x x p a a c a a x I I n na g b d l r

a-= = = = =

- (5)

where , , , (0, 1)a g d r Î and 1.b ³ These parameters represent the key factors of the prob-

lem and allow us to analyze various aspects of the solution. Here, a is a measure of risk

aversion, d represents the productivity of investment (effective use of investment), and r is

an investor’s output share. For our equilibrium solution ( , , ),n a I* * * since 1a* < with rea-

sonable parameter values, an increase in b tends to reduce the cost of effort ( ).c a* Hence,

b represents easiness of effort. Similarly, an increase in g tends to reduce the chance of

5 The results do not change if we use the following more general functions:

1( ) , ( ) , ( ) , ( ) , ( ) ,iu x Ax p a Ba c a Ca x I DI n E na g b d l r-= = = = =

where , , ,A B C D and E are arbitrary constants.

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success ( ).p a* Hence, g represents project riskiness. Since the ratio /g b often appears in

our formulas, we denote / .q g bº

Given the above parametric functions, we can solve for a closed-form solution of prob-

lem (4). The derivations are in the Appendix. The solution of the network capital is:

.(1 )

n dr ad

* =+

(6)

Then,

2 ( )(1 )( )(1 )

12 ( )(1 )( )(1 )

1 ,1 1

1 .1 1

I

a

b ggb g ad bdb g ad bd a

dad db g ad bdb g ad bd a

ad d g dr

ad b ad

ad d g dr

ad b ad

-- + -- + -* -

+ -- + -- + -* -

æ öæ ö+ - ÷ç÷ç ÷= ÷ çç ÷÷ ÷ç÷ç è ø+ +è ø

æ öæ ö+ - ÷ç÷ç ÷= ÷ çç ÷÷ ÷ç÷ç è ø+ +è ø

(7)

The syndicate’s output share is

.1

dl

ad* =

+ (8)

In contrast, if the network capital is exogenous (i.e., n is a given constant), with a corre-

sponding change to problem (4), the solutions of effort and investment are

( ) ( )

( ) ( )

( )(1 ) 1 ( )(1 )

1( )(1 ) 1 ( )(1 )

ˆ 1 ,

ˆ 1 .

I n n

a n n

gb gb g ad bd a b g ad bd

ad ddb g ad bd a b g ad bd

gr dr

b

gr dr

b

-- + - - - + -

+ -- + - - - + -

é ùê ú= -ê úë û


(9)

3.2. The Nash Investment Solution

In the above solution, the investors in the syndicate decide their investments coopera-

tively. Hence, we call the above solution the cooperative investment solution. Alternatively,

the investors in the syndicate may play a Nash game to determine their investments.6 The

solution in this case is called the Nash investment solution and investor i ’s investment is

determined by

6 We would like to acknowledge and thank an anonymous referee for proposing this alternative solution and

for suggesting that we compare syndicated investment with solo investment.

of 48

( )max ( ) ( ) .i

ii i j ijI

jj

IU p a u n x I II

lé ùê úº -ê úê úë û

åå

The FOC is

1( ) ( ) 1 ( )1 ( ) .

( )n x I n x Ip an I x I

al - é ùé ù ¢-ê úê ú= +ê úê úë û ë û

(10)

Then, the EN’s problem becomes

[ ]

[ ], ,

1

1

2

max 1 ( ) ( ) ( ) ( )

s t : 1 ( ) ( ) ( ) ( ),

( ) ( ) 1 ( ): ( ) 1.( )

n a In p a x I c a

IC n p a x I c a

n x I n x IIC p an I x I

a

l

l

l -

- -

¢ ¢. . - =

é ùé ù ¢-ê úê ú + =ê úê úë û ë û

(11)

Its solution is

(1 )(1 ) .

(1 )n d r d ad d

r ad* + - + -

=+

Then,

( )

( )

( )(1 ) 1 ( )(1 )

1( )(1 ) 1 ( )(1 )

(1 ) 1 .

(1 ) 1 .

I n n

a n n

gb g

b g ad bd a b g ad bd

d add

b g ad bd a b g ad bd

gr r d

b

gr r d

b

-- + -* * - * - + -

- +- + -* * - * - + -

é ù é ùê ú= - + -ë ûê úë û


If the network capital is exogenous, with a corresponding change to problem (11), the solu-

tions of effort and investment are

( )

( )

( )(1 ) 1 ( )(1 )

1( )(1 ) 1 ( )(1 )

ˆ (1 ) 1 ,

ˆ (1 ) 1 .

I n n

a n n

gb gb g ad bd a b g ad bd

ad ddb g ad bd a b g ad bd

gr r d

b

gr r d

b

-- + - - - + -

+ -- + - - - + -



3.3. Analysis

We analyze the solutions in this section. It turns out that the results derived from the

two alternative solutions are very similar. Hence, we present the results for the cooperative

of 48

investment solution only. Due to the space limit, we have only included the proof of Proposi-

tion 1 in the Appendix; other proofs are available upon request.

Syndication versus Solo

Is it possible to have a syndicated investment that is smaller than solo investment (i.e.

underinvestment)? Is it possible that incentive is worse under syndication? By denoting I

and a in (9) respectively as functions ˆ( )I n and ˆ( )a n of ,n we can compare solo investment ˆ(1)I with syndicated investment ˆ( ),I I n* *= and compare effort ˆ(1)a under solo investment

with effort ˆ( )a a n* *= under syndication. The question is: is it possible to have ˆ ˆ( ) (1)I n I* <

and ˆ ˆ( ) (1)a n a* < when 1?n* ³ It turns out that it is.

Proposition 1 (Syndication vs. Solo). Given c0ndition 1,n* ³ i.e., ,1

dr

ad£

+ for the

cooperative investment solution,

(a) Solo investment is larger than syndicated investment if and only if

1 ,1

dr q

ad£ - £

+ (12)

where / .q g bº

(b) Incentive under solo investment is better if and only if

1 .1

dq

ad- £

+ (13)

For example, if 0.1,a = 1.5,b = 0.8,g = 0.2r = and 0.8,d = the cooperative solu-

tion indicates underinvestment with syndication: 3.7,n* = ˆ( ) 4.9I n* = and ˆ(1) 5.1.I =

Similarly, for the same parameter values, the Nash investment solution also indicates under-

investment with syndication: 3.8,n* = ˆ( ) 50.5I n* = and ˆ(1) 64.7.I =

There are two inequality conditions in (12):

1 and 1 .1

dr q q

ad£ - - £

+

If and only if one of these inequality conditions fails will syndicated investment be larger.

The second inequality condition is the same as (13). This means that if the first inequality

condition holds, the EN’s incentive and investors’ investment are strategic complements in

equilibrium with respect to syndication; if the first inequality condition fails but the second

one holds, incentive and investment are strategic substitutes. In the latter case, solo invest-

of 48

ment is smaller, but incentive under solo investment is better. In the following, we provide

intuition for the results in Proposition 1. We focus on investment only; intuition for incentive

is similar.

On the one hand, with a solo investor, although sources of funding are limited, her in-

centive is good since she is the sole recipient of the income share for investors and hence

may invest a lot. On the other hand, with syndication, although there are multiple sources of

funding, each investor’s willingness to invest is low since the investors have to share the

benefits and hence the total investment may be low. Both the EN and the investors care

about output shares, but while the EN welcomes more investment, the investors prefer to

invest less. Depending on project risk, risk aversion, productivity and cost of effort, each

party may have a tendency towards one objective or the other. In cases where the EN does

not care so much about the investment amount, for example, if productivity is high (in terms

of effective use of funding), solo investment may be larger than syndicated investment. Our

theory indeed suggests this. Condition (12) is more likely to hold if d is large; if so, solo

investment is larger than syndicated investment.

One important function of the syndicate is to share risk. If risk aversion is low, the syn-

dicate’s role of risk sharing is reduced, while output sharing within the syndicate will still

have a negative effect on investment. Hence, if risk aversion is low, solo investment may be

larger than syndicated investment. Our theory indeed confirms this. Condition (12) is more

likely to hold if a is small; if so, solo investment is larger than syndicated investment. On

the other hand, if risk aversion is high, a solo investor will invest conservatively, while syndi-

cation allows risk sharing so that investors will be more willing to invest. In this case, we

expect syndicated investment to be larger than solo investment. Indeed, when a is large,

condition (12) is more likely to fail; if so, our theory predicts that syndicated investment is

larger.

If each investor only has a small output share ,r each will invest a small amount. Then,

for a given required amount of investment, the syndicate will need to be large. Such a syndi-

cate tends to bargain for a large share of output, causing a negative effect on incentive, which

in turn reduces investment. Hence, in this case, solo investment is likely to be larger than

syndicated investment. Our theory indeed confirms this. Condition (12) is more likely to hold

if r is small; if so, solo investment is larger than syndicated investment.

When the project is highly risky, we expect a preference for syndication on both sides.

Indeed, when the project is risky as represented by a large ,g condition 1r q£ - in (12)

tends to fail, implying a larger syndicated investment.

of 48

If effort is costly, the EN will rely more on investment than her own effort, in which case

she is likely to go for syndication. Indeed, if b is small, condition 1r q£ - in (12) tends to

fail; if so, syndicated investment is larger.

Proposition 2 (The Gap between Syndicated and Solo Investments). Given c0ndition

1,n* ³ for the cooperative investment solution,

(a) If 11

dq

ad- >

+or 1 ,

1d

r qad

£ - £+

higher productivity implies a larger gap be-

tween syndicated investment and solo investment.

(b) If 11

dq

ad- >

+ or 1 ,

1d

r qad

£ - £+

higher risk aversion implies a smaller gap

between syndicated investment and solo investment.

(c) If 1 ,r q³ - a larger r implies a larger gap between syndicated investment and solo investment; otherwise the gap is smaller.

Network Capital

Interestingly, g and b are irrelevant to the equilibrium network capital, even though

the equilibrium investment and effort are dependent on these two factors. Here, b repre-

sents easiness of effort and g represents project riskiness, both of which depend crucially on

the EN’s effort. This suggests that those factors directly related to the EN’s effort do not have

an effect on network capital.

In contrast, the network capital is heavily dependent on the risk aversion a and produc-

tivity d of investment, both of which depend crucially on investors and investment. This

suggests that those factors directly related to investment influence network capital strongly.

Proposition 3 (Network Capital).

(a) The syndicate size or network capital is diminishing in risk aversion, and this negative

effect of risk aversion on syndicate size is also diminishing in risk aversion:

2

20, 0.n na a

* *¶ ¶< >

¶ ¶ (14)

(b) The syndicate size or network capital is increasing in productivity, and this positive

effect of productivity on syndicate size is also diminishing in productivity:

of 48

2

20, 0.n nd d

* *¶ ¶> <

¶ ¶ (15)

Proposition 3 suggests that more risk aversion implies a smaller syndicate. This result

makes sense since highly risk-averse investors demand high compensation for their invest-

ment. Consequently, the EN prefers a small syndicate to reduce the investors’ bargaining

power for compensation. Proposition 3 also indicates that for a project with high return

potential, the EN will pick a lead investor to organize a large syndicate. This result is fairly

intuitive.

Output Sharing

We now investigate how the two parties share output.

Proposition 4 (Sharing). Regarding the syndicate’s output share ,l* we have

2 2

2 20, 0; 0, 0.l l l la a d d

* * * *¶ ¶ ¶ ¶< > > <

¶ ¶ ¶ ¶ (16)

That is, the more risk averse the investors are, the smaller the output share they will collec-

tively get; and the more productive the investment is, the larger the output share the inves-

tors will collectively get.

A smaller output share for more risk-averse investors is a consequence of less bargaining

power implied by (14). At the same time, a larger output share for the EN induces the EN to

invest more effort. This suggests that providing better incentive for the EN is an effective

strategy to cope with investor risk aversion. Further, if investment is more productive (more

effective use of investment), the investors are given a larger output share, which encourages

them to invest more in the project.

Investment and Incentives

We now investigate the effects of risk aversion, productivity and an investor’s output

share on incentive and investment.

While l is the output share of the syndicate, r is the output share of each investor. For

example, if the syndicate has a 50% share of the output and there are five investors ( 5),n* =

each investor is entitled to 50% / 10%nr *= = of the output. This r reflects each investor’s

bargaining power, which tends to have a negative effect on the EN’s incentive. The effect of

r is clear from (6) and (7): an increase in the investor share r reduces the syndicate size,

of 48

effort and investment. The reason is that a larger investor share reduces the EN’s incentive,

which in turn reduces investment; consequently the EN will choose a smaller syndicate size.

The effects of risk aversion and productivity are summarized by the following two

propositions.

Proposition 5 (The Effect of Risk Aversion on Investment and Incentive).

(a) Investment generally increases with risk aversion. Specifically, investment increases

with risk aversion if and only if

( ) ( )[ ] ( )( )

2

111 1 1

2 1 11 111 1 .e

dad

qqad d add q qqr d ad ad d q

æ ö÷ç + - ÷ç ÷çè ø--- -- + - +- --£ + + - (17)

(b) Incentive generally improves with risk aversion. Specifically, incentive improves with

risk aversion if and only if

( ) ( )[ ]1 1 1

21 111 1 .q

d q qqr d ad ad d q- --- --£ + + - (18)

Typically /q g bº is small since b is larger than 1. Hence, we will generally have

1 .d q< - If so, Proposition 5(a) can be expressed as 0Ia

*¶³

¶ if and only if

( ) ( )[ ] ( )( )

2 1 11

1

111

2 1 111.

1 1 ed q

dad

qqad d adqq

rd ad ad d q

--

æ ö÷ç + - ÷ç ÷÷çè ø---- + - +--

ì üï ïï ï£ í ýï ï+ + -ï ïî þ

With reasonable parameter values (where a assumes values between 0 and 1), the right-

hand side of the above inequality is above 70. Hence, condition (17) generally holds. This

means that investment generally increases with risk aversion. By the same reasoning, incen-

tive generally improves with risk aversion.

The explanation is that risk aversion puts pressure on performance, which improves in-

centive and in turn induces more investment. Higher risk aversion also reduces the syndicate

size and hence results in a larger output share for the EN, which also improves incentive.

One interesting observation here is that more risk-averse investors end up investing more in

equilibrium.

Proposition 6 (The Effect of Productivity on Investment and Incentive).

(a) Investment increases with productivity if and only if r is small. Specifically, invest-

ment increases with productivity if and only if

of 48

( )( )

11 22 1 1(1 ) (1 ) 1 1 11 .

1 1e

qad q da q qa q

a q a qa d ad d adad d dr q

ad ad

æ öæ ö+ ÷ ÷ç ç- - - -÷ ÷ç ç- ÷ ÷÷ ÷ç çè øè ø- - + + - +æ öæ ö+ - ÷ç÷ç ÷£ ÷ çç ÷÷ ÷ç çè ø è ø+ +

(19)

(b) Incentive is generally decreasing in productivity. Specifically, incentive is decreasing in

productivity if and only if

112 (1 ) (1 )1 .

1 1e

qda da q

a a qd ad dr q

ad ad

+ ---

æ ö æ ö+ -÷ç ÷ç÷³ ÷ç ç÷ ÷÷ç çè ø è ø+ + (20)

For reasonable parameter values, the right-hand side of (19) is between 0 and 10, and

the right-hand side of (20) is less than 0.17. Hence, investment is increasing in productivity

if and only if r is small, and incentive is generally decreasing in productivity. There are two

reasons for these results. On the one hand, since a larger investor output share r has a

negative effect on incentive, r cannot be too large for the EN to have enough incentive. If the

investor share is small, with sufficient incentive, the EN welcomes higher productivity and

applies more effort, which in turn induces investors to invest more. On the other hand, a

large investor share sufficiently dampens the EN’s incentive; in this case, with insufficient

incentive, higher productivity puts less pressure on the EN to perform, which implies less

incentive and investment.

Cost of Effort and Project Risk

We now investigate the effects of easiness of effort and project riskiness on investment

and incentive.

Proposition 7 (The Effects of Easiness of Effort and Project Riskiness).

(a) Investment is generally positively associated with easiness of effort and negatively

associated with project riskiness. Specifically, an increase in easiness of effort b or a

decrease in project riskiness g raises investment if and only if

11(1 )(1 )21 .

1 1e

ad dq ad daad

adad d dr q

ad ad

+ -- + -æ öæ ö+ - ÷ç÷ç ÷³ ÷ çç ÷÷ ÷ç çè ø è ø+ +

(21)

(b) Incentive is generally negatively associated with project riskiness. Specifically, a de-

crease in project riskiness g improves incentive if and only if

11(1 )(1 )12

11 .1 1

ead d

q ad dad daadadq adad d d

r qad ad

+ -- + -+ -

+æ öæ ö+ - ÷ç÷ç ÷³ ÷ çç ÷÷ ÷ç çè ø è ø+ +

(22)

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(c) Incentive is generally positively associated with easiness of effort. Specifically, an in-

crease in easiness of effort b improves incentive if and only if (21) holds.

For reasonable parameter values, the right-hand sides of (21) and (22) are less than

0.02 and 0.06, respectively. Hence, these two conditions generally hold. Since 1a* < with

reasonable parameter values, if a* is fixed, an increase in b will reduce the cost of effort

( ).c a* Hence, we expect an increase in b to raise effort, which in turn encourages more

investment. There is a second effect: an increase in effort will raise the cost of effort ( ).c a* In

fact, ( )c a* does increase with b when a* is allowed to change with .b However, this second

effect is a consequence of the first effect. This means that the second effect cannot change the

fact that a* is increased; it can only reduce the extent of this increase. The net effect (the

total of the two effects) is indicated in Proposition 7, i.e., an increase in b raises effort and

investment.

Similarly, since 1,a* < if a* is fixed, an increase in g will reduce the chance ( )p a* of

project success. In fact, ( )p a* is still decreased when a* is allowed to change with .g Hence,

as indicated in Proposition 7, a decrease in g improves the chance of success or reduces

project riskiness, which in turn boosts investment and improves incentive.

So far, we have considered the usual circumstances for the results in Propositions 5–7.

Under some unusual circumstances, when the inequality conditions fail, the conclusions can

be reversed. For example, for Proposition 7(b), if r is sufficiently small, condition (22) fails,

so that incentive is positively associated with project riskiness .g To explain this result, we

need to understand the three underlying forces at work. First, an increase in project riskiness

g has a negative effect on incentive. Second, a small r (a small investor output share) has a

positive effect on incentive. Third, as indicated in Proposition 7(a), an increase in project

riskiness implies less investment, which may put pressure on the EN to perform, implying a

positive effect on incentive. Here, we cite the fact that incentive and investment may be

strategic substitutes in equilibrium. In aggregate, when r is small enough, the positive effect

from a small r and/or from the pressure of reduced investment may dominate, which leads

to an improvement in incentive. Hence, in Proposition 7(b), a positive association between

incentive and project riskiness is possible. Similar situations apply to the other results too.

of 48

Endogenous vs Exogenous Networks

One natural question to ask is whether the type of networks, either endogenous or ex-

ogenous, is important in our results. In Figure 1, we graph investment by arbitrarily setting

0.2,r = 0.5,g = 2b = and allowing risk aversion to change; in Figure 2, we regraph

investment with the same parameter values except a fixed 0n at an equilibrium value. Com-

paring Figures 1 and 2, we find that productivity has opposite effects on investment in the

two figures. In other words, with an endogenous network in Figure 1, productivity has a

positive effect on investment; but with an exogenous network in Figure 2, productivity has

a negative effect on investment. Hence, the endogeneity of network is important in our con-

clusions.

0.01

0.02

0.03

0.04

0.24 0.26 0.28 0.3 0.32a

I *

0.3d =

0.5d =

0.06

0.07

0.08

0.09

0.1

0.11

0.24 0.26 0.28 0.3 0.32a

I

0.3d =

0.5d =

Figure 1. Investment with an Endogenous Network Figure 2. Investment with an Exogenous Network

4. Empirical Evidence from VC Investments

Our theory is applicable to many kinds of investments. With the guidance of our theory,

in this section, we conduct an empirical analysis of the determinants of the syndicate size

using U.S. VC investment data.

Syndication is widely observed in VC investments. In fact, VCs typically syndicate their

investments with other VCs, rather than investing alone (Lerner, 1994). The role of syndica-

tion has been investigated theoretically and empirically in the literature. Casamatta and

Haritchabalet (2007) suggested in theory that syndication improves the screening process of

VC deals and prevents competition among investors after investment opportunities are

disclosed. Using a sample of Canadian companies, Brander et al. (2002) provided evidence

that syndicated VC investments have higher returns. Our theory focuses on the endogenous

of 48

formation of investment syndicates in equilibrium. It is unique in that it determines the lead

investor’s network capital endogenously, implying a testable formula for network capital.

We focus mainly on the determinants of network capital or syndicate size, which is the

key in our theoretical model. As shown in equation (6), the determinants of the syndicate

size or the lead VC’s network capital ( n ) include the lead VC’s risk aversion ( a ), productivity

(d ) and the lead VC type ( r ). Based on this, we formulate the following regression model:

0 1 2 3 .Dependent Variable Investment Risk Portfolio Company Quality Controlsa a a a= + + +

Here, the dependent variable is the syndicate size or the lead VC’s network capital. Our

theoretical model indicates that the lead VC’s network capital is endogenously determined in

the syndication process. In other words the EN chooses the optimal syndicate size as well as

the lead VC with a certain network capital which is in fact a tradeoff between future funding

and profit allocation. We take the ex post “Investment Risk” as a proxy for the lead VC’s risk

attitude. The higher the lead VC’s risk aversion, the lower the ex post investment risk. “Port-

folio Company Quality” is taken to be a proxy for productivity. The higher the portfolio com-

pany quality, the greater the productivity. “Controls” include lead VC type plus a set of other

control variables.

Equation (6) implies a negative relationship between the syndicate size and the lead

VC’s risk aversion, and a positive relationship between the syndicate size and the firm’s

productivity. Hence, we expect both investment risk and portfolio company quality to be

positively related to the syndicate size.

4.1. Data and Variables

Our sample was obtained from the SDC VentureXpert database, which is the main pub-

lic database for academic research on VC. We collected data on all the VC investments by U.S.

VCs in U.S. portfolio companies that received their initial VC funding during the period

1985–2005. We focused on VC investments that were made in the development stage of a

portfolio company. Therefore, we excluded those investments made in the mature stages,

including investments in “Buyouts/Acquisitions,” “unknowns” and those made by private

equity, such as angel or buyout funds. We also excluded those observations without regres-

sion variables. We eventually identified 40,395 VC investment rounds in 15,264 portfolio

companies.

Table 1 presents the distribution of our sample by funding year and the industry, loca-

tion and development stage of the portfolio company. The number of observations and the

corresponding percentages are also given. As observed, VC investments increased rapidly

of 48

since 1994, peaked in year 2000, and slowed down considerably following the “bubble burst”

of the dot-com era. The sample covered the following 18 industries based on the venture

economics industry classification (VEIC) code in the VentureXpert database: agricul-

ture/forestry/fishing, biotechnology, business services, communications, computer hard-

ware, computer other, computer software, construction, consumer related, financial services,

industrial/energy, internet specific, manufacturing, medical/health, semiconductor

/electronics, transportation, utilities, and other. Clearly, VC investments were concentrated

in high-technology industries. In particular the computer software, internet specific, medi-

cal/health, and communications industries constituted respectively 23.0%, 18.3%, 12.9% and

11.3% of the whole sample.

Regarding the locations of the portfolio companies, we can see a clear trend of geo-

graphic clustering in VC investments. For this reason, we report only the top 20 states in

which VC investment rounds have been made. The other 30 states constituted only 7.2% of

the sample. We found that most VC investments occurred in California, Massachusetts,

Texas and New York, which constituted respectively 36.8%, 11.4%, 5.8% and 4.5% of the

sample. That’s a total of almost 60% of our sample. Also, about 40% of the VC investment

rounds were made in the seed or early development stage of a portfolio company, which is

comparable with the 39% reported by Gompers (1995).

The definitions and measures of all the variables are defined and explained in Table 2.

The variables are defined in the remainder of this section.

Dependent Variables

Our unit of analysis is a VC investment round. The dependent variable is the logarithm

of the number of VCs participating in an investment round and is named Syndicate Size. For

each VC investment round, we identified the lead VC as the VC firm that injected the largest

funding. In practice, the lead VC is typically the most active investor and plays a leading role

in monitoring and professionalizing a portfolio company. Our definition of the lead VC is

similar to those of SØrensen (2007), Hochberg et al. (2007) and Nahata (2008). In total,

there were 2,373 lead VCs in our sample.

The network capital in our theoretical model can be in many forms, including other VCs,

head hunters, patent lawyers and investment bankers. In the spirit of Hochberg et al. (2007),

we focused on the most important coinvestment network. We measured a lead VC’s network

capital in a given investment round by the number of VCs that she had syndicated with

during the five years prior to the investment round, normalized it by the number of active

VCs participating in at least one investment round during the five-year span and named it

of 48

Network Degree. Network Degree is an indirect measure of a lead VC’s network capital. The

more coinvestment ties a lead VC has, the more opportunities exist for exchange and so the

more influential the lead VC. A lead VC who has many coinvestment ties with other VCs may

have access to a wide range of experts, contacts and pools of capital. To further analyze a lead

VC’s direct relationships with other VCs, we constructed two alternative variables indicating

the lead VC’s network capital in a given investment round. Specifically Network Outdegree

and Network Indegree are measured respectively as the normalized number of VCs a lead

VC had invited into her syndicates and the number of VCs who had invited the lead VC into

their syndicates in the five years prior to the investment round. These three measures repre-

senting the lead VC’s network capital are the same as those used by Hochberg et al. (2007).

For example, if a lead VC had syndicated with 10 different VCs, had invited five different VCs

into her syndicates and had been invited into four different VCs’ syndicates during 2000–

2004, and if there were a total of 21 active VCs participating in at least one investment deal

during 2000–2004, the values of Network Degree, Network Outdegree and Network Inde-

gree of the lead VC for those investment rounds occurring in 2005 would respectively be

50% (10/(21-1)), 25% (5/(21-1)) and 20% (4/(21-1)).

Investment Risk

Investment risk was used to represent a lead VC’s risk version ( a ). The first measure of

investment risk in an investment round, named Company Age, is the logarithm of the age of

a portfolio company at the time of the investment round, while the age of a portfolio com-

pany at the time of the investment round is the number of years between its founding and

the year of the investment round. Hence, a younger company is likely to be riskier.

It is widely observed that VCs typically target certain industries, certain development

stages of the portfolio companies, or certain local geographical areas (Bygrave, 1987; Gupta

and Sapienza, 1992; Norton and Tenenbaum, 1993). This may help them control risk when

identifying, evaluating and monitoring projects and prevent competition from other VCs and

other types of financial institutions. Our sample distribution in Table 1 also implies such

investment clustering. In the spirit of Sorenson and Stuart (2001), investment risk was de-

termined by industry distance, stage distance and geographic distance between a lead VC

and her portfolio company. A lead VC who makes an investment in a faraway portfolio com-

pany, a new industry, or a new development stage of a portfolio company is bearing more

investment risk than most and so she must be less risk averse.

We measured the Industry Distance of a given investment round by the percentage of

investment rounds a lead VC had made from 1980 to the year prior to the given investment

of 48

round that were not in the same industry as the portfolio company. There are totally 18

industry groups based on the VEIC code. This measure incorporates at least five years of VC

investment experience. For a VC investment round that occurred in 2000, this measure of

industry distance incorporates 20 years of VC investment experience during 1980–1999. For

example, if the SDC VentureXpert database shows that a lead VC had made a total of 100

rounds of investment during 1980–1999 and 15 of those were in the “Computer Hardware”

industry, the Industry Distance of this lead VC for an investment round made in 2000 and

in a portfolio company in the “Computer Hardware” industry would be 85% ((100-15)/100).

Similar to Industry Distance, we measured the Stage Distance of a given investment

round by the percentage of investment rounds a lead VC had made from 1980 to the year

prior to the given investment round that were not in the same development stage as the

portfolio company in the given round. We covered four development stages: seed stage, early

stage, expansion stage and later stage. As a robustness check, we also measured Industry

Distance and Stage Distance by past investment amount rather than by the number of past

investment rounds. All the results are similar. Finally, we measured Geographic Distance

directly by the logarithm of the physical distance between the state in which the lead VC is

located and her portfolio company.

Portfolio Company Quality

We took the quality of a portfolio company as a proxy for project productivity ( d ) in the

theoretical model. The greater the total VC investment, the higher the portfolio company

quality is likely to be, and the higher the likelihood of good performance. Gompers (1995)

proposed that funding in follow-on rounds is given only if a portfolio company does well in

earlier rounds. Also, specific milestone-contingent clauses are contained in most VC financ-

ing contracts, by which VCs automatically cease to provide further funding to weak ventures

(Wang, 2009). Hence, a larger VC funding reflects better quality of the portfolio company.

Following Nahata (2008), we used the logarithm of the total VC funding amount in a portfo-

lio company across all financing rounds as a proxy for its quality and named it Total VC

Funding.

We also defined an indicator variable on whether a portfolio company has successfully

exited through an IPO or acquisition as a proxy for its quality and named it Quality Indica-

tor. In practice, observable VC returns are mainly made from successful exits, such as if the

portfolio company goes public or is acquired (Cumming and MacIntosh, 2003; Cochrane,

2005). The larger the number of successful exits a VC makes from its portfolio companies,

the larger its internal rate of return from investments. Hence, we also used Quality Indicator

of 48

to represent portfolio company quality. We traced the exits of portfolio companies until the

end of 2009, which provides a minimum of four years for a successful exit.

These two measures of company quality are by no means perfect and involve a look-

ahead bias since the cumulative funding and a successful exit are unknown at the time of

early financing rounds. However, considering that VentureXpert provides little information

on portfolio companies other than financing rounds, funding amount, investors and exits,

these two measures have been well adopted in the literature and have been considered to

reflect many unobservable factors that determine a portfolio company’s prospects at the time

of funding.

Control Variables

Other than the explanatory variables indicating investment risk and portfolio company

quality, we also needed to control for lead VC type based on its organizational structure.

There is a distinction between traditional VCs and the so-called captive VCs. The latter are

affiliated with corporations, financial institutions or governments (Bottazzi et al., 2008;

Nahata, 2008; Hellmann et al., 2008). Different types of VCs may have different resources

and connections with other institutions and emphasize different strategic objectives. To

control for lead VC type, we created three dummy variables indicating whether a lead VC was

affiliated with a corporation, an institution, or a government, and named them Corporate VC

Indicator, Institutional VC Indicator and Government VC Indicator, respectively.

We also included industry indicators based on the VEIC code to partially account for

technological and industrial characteristics of portfolio companies. We further included

funding year indicators as additional control variables. Considering the possible effect of an

early choice of syndication on later rounds, we further controlled for the round sequence

effects based on the sequencing of investment rounds in each portfolio company (being in

the first, second or third round, etc.).

4.2. Summary Statistics and Correlations

Table 3 presents summary statistics of all the regression variables.7 The quartiles, means,

standard deviations and the number of observations are presented. As indicated, about 2.4

VCs formed a syndicate in an investment round on average, suggesting the popularity of

7 We reported raw values for all the variables in Table 3, even though some of them were used in their natu-

ral logarithm form in our regressions (as indicated by “**” in Table 2).

of 48

syndication in VC investment. About 54% of VC investment rounds were syndicated (not

tabulated). A typical lead VC syndicated with 7.48% of all active VCs (Network Degree) on

average, invited 4.71% of all active VCs to her syndicates (Network Outdegree), and was

invited by 1.37% of all active VCs to their syndicates (Network Indegree) in the five years

prior to the current investment round. The lead VCs in our sample had higher network capi-

tal on average than those reported by Hochberg et al. (2007). In particular, Hochberg et al.

(2007) reported the averages of Network Degree, Network Outdegree and Network Inde-

gree to be 4.24%, 1.20% and 1.00%, respectively. The reason for the difference is that we

measured the network capital for the lead VCs only, who tend to have more network capital

and their network capital tends to be more influential than an average VC.

Table 3 indicates high investment risk in the VC market. On average, a portfolio com-

pany was less than five years old with the median being only three years old. A trend in

specialization is clear. In an investment round, on average 20% (or 32.5%) of a lead VC’s

investment experience was in the industry (or in a development stage) of the portfolio com-

pany. In other words, the average Industry Distance was 80% (with a standard deviation of

24%), which is very close to the 77% (with a standard deviation of 21%) reported by Sorenson

and Stuart (2001). The distribution of Stage Distance was similar to that of Industry Dis-

tance, whose mean and standard deviation were 67.54% and 21%, respectively. The average

geographic distance between a lead VC and her portfolio company was about 1,208 kilome-

ters with the median being only 363.9 kilometers. Also, 41% of VC investment rounds were

made in the same state as the lead VC’s (unreported). For portfolio companies, the total VC

fund inflows across all rounds were 22.27 million dollars on average,8 which is comparable

with the 24 million dollars reported by Nahata (2008). As observed, 38% of VC investments

made successful exits through IPOs or acquisitions by the end of 2009, which is slightly

higher than the 35% reported by Gompers (1995) for the period 1961–1992. Finally, the

probabilities that a lead VC was affiliated with a corporation, a financial institution and a

government were respectively 3%, 4% and 11%.

The Spearman and Pearson correlation matrices are tabulated respectively in the upper

and lower diagonals of Table 4. The correlations among all the variables were small, except

for those among the three alternative measures of the network capital of the lead VC, namely

Network Degree, Network Outdegree and Network Indegree, which suggests the absence of

severe multicollinearity in our regression model.

8 The value of Total VC Funding reported in Table 3 was based on VC investment rounds, which is slightly

different from the value based on portfolio companies.

of 48

4.3. Regression Results

We also investigated the impact of investment risk and portfolio company quality on the

syndicate size (which also indicates the network capital of a lead VC in equilibrium in our

theoretical model). Our unit of analysis was a VC investment round. The sample size was

40,395. We took Syndicate Size and the three alternative measures of the network capital of

the lead VC, namely Network Degree, Network Outdegree and Network Indegree, as the

dependent variables. We employed an OLS model to relate the dependent variables with the

following primary explanatory variables: investment risk as measured/proxied by Company

Age, Industry Distance, Stage Distance and Geographic Distance, and portfolio company

quality as measured/proxied by Total VC Funding and Quality Indicator. We also controlled

for lead VC type by including Corporate VC Indicator, Institutional VC Indicator and Gov-

ernment VC Indicator in all the regressions. Although not reported, in all the regressions, we

also included 20 funding year indicators, 17 industry indicators based on the VEIC codes and

19 round sequence indicators based on the sequencing of investment rounds in each portfo-

lio company (being in the first, second or third round, etc.) to control for the year, industry

and round sequence fixed effects.

Table 5 reports the results. All the t-statistics have been adjusted for heteroskedasticity

(White, 1980). In models 1 and 2, we took Syndicate Size as the dependent variable and

separately included factors representing investment risk and portfolio company quality. In

models 3 to 5, we separately took the three alternative measures of the network capital of a

lead VC as the dependent variable and included all the explanatory variables. We found very

similar results in all the models. Our empirical results are consistent with our theoretical

findings.

Our theoretical model implies a negative relationship between a lead VC’s risk aversion

( a ) and the syndicate size ( n ). Our regression results confirm this prediction by showing

that investment risk had a positive impact on the syndicate size. Also, the coefficient of Com-

pany Age was negative at the 1% significance level and the coefficients of Industry Distance,

Stage Distance and Geographic Distance were all significantly positive at the less than 5%

significance level. These results are also consistent with the prediction of our theoretical

model.

For the magnitude of the effects, we found that a one standard deviation increase in

Company Age decreases Syndicate Size and its three alternative measures, Network Degree,

Network Outdegree and Network Indegree, by 1.83%, 48.31%, 22.82% and 8.97%, respec-

tively. Also, a one standard deviation increase in Industry Distance (Stage Distance, Geo-

graphic Distance) increases Syndicate Size and its three alternative measures, Network

of 48

Degree, Network Outdegree and Network Indegree, by 3.29% (1.40%, 2.11%), 108.81%

(12.10%, 37.13%), and 18.18% (3.08%, 1.49%), respectively.

Our theoretical model implies that productivity ( d ) has a positive impact on a lead VC’s

equilibrium network capital ( n ). Hence, we expect a positive relationship between portfolio

company quality and the syndicate size in our regressions. Indeed, the coefficients of Total

VC Funding and Quality Indicator were both positive at the 1% significance level. Specifi-

cally, a one standard deviation increase in the total VC funding across all rounds for a portfo-

lio company increases Syndicate Size and its three alternative measures, Network Degree,

Network Outdegree and Network Indegree, by 19.91%, 108.42%, 64.07% and 15.02%, re-

spectively. Also, a one standard deviation increase in the likelihood of a successful exit im-

plies an increase in Syndicate Size and its three alternative measures, Network Degree,

Network Outdegree and Network Indegree, of 6.05%, 32.83%, 22.46% and 4.08%, respec-

tively.

Since lead VC type ( r ) in our theoretical model can be measured by a set of characteris-

tics of the lead VC in our empirical model, our theory predicts an impact, but not the specific

signs of the coefficients of those variables representing the lead VC’s characteristics. Indeed,

as expected, our regressions indicate that both Corporate VC Indicator and Government VC

Indicator had a negative impact, but Institutional VC Indicator had a positive impact, on

Syndicate Size.

In summary, after controlling for lead VC type and the fixed effects of funding year, in-

dustry and round sequence, we found that both investment risk and portfolio company

quality had a significant positive effect on syndicate size. This empirical finding is consistent

with our theoretical finding.

4.4. Robustness Checks

To ensure the reliability of our empirical analysis, we conducted many robustness

checks. Firstly, we investigated the impact of investment risk and portfolio company quality

on the syndicate size at the portfolio company level to rule out the double counting problem.

The unit of analysis became a portfolio company, rather than a VC investment round. We

defined Syndicate Size as the number of VCs providing funding to a portfolio company. The

lead VC was identified as the VC that participated in the initial round of financing and made

the largest total investment in the portfolio company across all rounds. The lead VC’s net-

work capital was measured similarly as before but this time we took its value at the time a

portfolio company received initial VC funding. With a reduced sample size of 15,264, all our

results remained qualitatively the same after these adjustments.

of 48

Secondly, we also tried many alternative measures of investment risk and portfolio

company quality. For example, we measured Industry Distance and Stage Distance based on

the past investment amount rather than the number of past investment rounds. We rede-

fined Geographic Distance as a dummy variable indicating whether a lead VC and her port-

folio company were located in the same state. We further included public companies’ risk as

a proxy for the investment risk borne by these private companies. Specifically, we first iden-

tified the 4-digit SIC code for each portfolio company based on the VEIC-SIC concordance

provided by Dushnitsky and Shaver (2009). Then we calculated the standard deviation of the

ROA, ROE and stock returns of public companies using accounting and stock information

from Compustat and CRSP with the same 2-digit SIC code of the portfolio company in the

year prior to a VC investment round. Lastly we took these industry risk variables of the pub-

lic companies as proxies for the investment risk of the VC investment round. All our findings

remained unaltered.

On portfolio company quality, around 25% of the portfolio companies voluntarily re-

ported their market valuation after an investment round, which is a good predictor of their

quality. Even though we do not know exactly the reasons for disclosing company market

valuation, we argue that portfolio companies with better quality are more likely to disclose

their market valuation. It is widely suggested in the accounting literature that voluntary

information disclosure plays a role in mitigating asymmetric information and agency prob-

lems (Myers and Majluf, 1984). This reduces the cost of capital (Botosan, 1997) and IPO

underpricing (Leone, et al., 2007) and increases market capitalization of earnings (Piotroski,

1999). Therefore, we used a dummy variable indicating whether a portfolio company dis-

closes its post-round market valuation as one more proxy for company quality. We found

that this variable had a positive effect on Syndicate Size at the 1% significance level. Again,

all our existing results remained unchanged.

Thirdly, to investigate further whether our results were unduly influenced by outliers,

we re-ran our regressions after winsorizing the top and bottom 1%, 2% and 5% for each

variable. The results remained largely similar.

Fourthly, considering the possible impact of the NASDAQ bubble during 1999–2000, we

re-ran our regressions by excluding these two years. The sample size was reduced to 31,368.

Our results were qualitatively unchanged.

Finally, as shown in Table 1, the computer software industry and the California state

made the largest contributions to our dataset respectively in terms of the portfolio company

industry and location. To examine whether the inclusion of these special subsamples influ-

enced our results, we ran our regressions yet again after excluding the software industry or

of 48

the California state, which reduced the sample size respectively to 31,115 and 27,731. The

results again remained qualitatively unchanged.

5. Conclusion

As an effective investment strategy, investors often form a syndicate to invest jointly in a

company. The unique feature of this paper is that it endogenizes the formation of the in-

vestment syndicate. We provide a theory on endogenous networks in investment syndication

and analyze how several key factors such as risk aversion, productivity, risk and cost affect

the incentives for and the investments by managers and investors. Since investment syndica-

tion is very popular in VC investments, we also apply our theory to VC investments and

identify empirical evidence in support of our theory.

Unlike previous empirical papers on investment syndication or investment networks

which have mostly focused on the role of the lead investor (such as Brander et al., 2002;

Hochberg et al., 2007, 2010; Casamatta and Haritchabalet, 2007), this paper focused instead

on strategic interactions between managers and investors. In our model, investment deci-

sions, together with syndication and network, are determined in equilibrium in three stages.

Most of the existing studies have focused only on the second stage. In addition, we demon-

strated that network endogeneity is crucial. For example, productivity can have opposite

effects on investment if the network is treated as exogenous instead of endogenous (Figures 1

and 2).

We have also applied our theory to VC investments. Using 40,395 domestic VC invest-

ment rounds made in 15,264 U.S. portfolio companies by U.S. VCs during 1985–2005 and

controlling for various factors, we found empirical support for our theory.

Syndication occurs in many domains, including the VC industry, IPOs, bond issuing, re-

al estate development, and large infrastructure projects (subways, railways, roads and air-

ports). Although our empirical work focuses on VC, insights from our study provide an un-

derstanding of syndication as a form of network in general.

Appendix

In this appendix, we give the derivations for the expressions in (3), (6)–(8) and (9).

of 48

A.1. Derivation of (3)

The FOC for 1I is

( )

( )

11 11 2

22

1 ( ) ( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) ( ) ( ) .

jj

jjjj

ni i i

ii jjjj

I II Ip a u n x I n x I n x II II

I I Ip a u n x I n x I n x II II

l l l

l l l=

ì üï ï-é ù ï ïï ï¢ ¢ê ú= +í ýê úë û ï ïï ïï ïî þé ù ì üï ïï ï¢ ¢ê ú+ - +ï ïí ýê úë û ï ïï ïï ïî þ

ååå

å åå

With the same risk aversion a for all the investors, we must have iI nI= for all i in equilib-

rium. Then,

{ }

{ }

1 2

22

1

11 11 ( ) ( ) ( ) ( ) ( ) ( ) ( )

1 1( ) ( ) ( ) ( ) ( ) ( ) ( )

1 1 1( ) ( ) ( ) ( ) ( ) ( ) ( )

1( ) ( ) ( )

n

ii

i

I Inp a u n x I n x I n x I

n I nIp a u n x I n x I n x I

n nI nnp a u n x I n x I n x I

n nI n

p a u n x In

l l l

l l l

l l l

l

=

ì üï ïï ï-ï ïé ù í ý¢ ¢ê ú= +ï ïï ïê ú ï ïë û î þé ù

¢ ¢ê ú+ - +ê úë û

é ù -¢ ¢ê ú= +ê úë û

é¢ ê+ë

å

{ }2

1 1( ) ( ) ( ) ( ) ,n

in x I n x I

nI nl l

=

ù¢ú - +

ê úûå

implying

[ ]11

1 1( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) .n

ii

nI n n p a x I u n x I p a u n x I I n x I n x In n

l l l l l=

é ù é ù¢ ¢ ¢ê ú ê ú= + -ê ú ê úë û ë û

å

With the same utility function for all, we have

[ ]1 1( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ,nI n n p a x I n x I p a n n x I I n x I n x In n

a a

l l l l l- -é ù é ù

¢ê ú ê ú= + -ê ú ê úë û ë û

implying

1 1( ) ( ) ( ) ( ) ( ) 1 ,

( ) ( )I n x I n x I Ix I

p a n n n x I

a al l- - é ù¢é ù é ùê úê ú ê ú= + -ê úê ú ê úë û ë û ë û

which implies (3).

A.2. Derivation of the Solution (6)–(8)

Condition 2IC implies

of 48

1

1( ) .n a n In

ag d adl

d-

- +é ùê ú =ê úë û

(23)

By this, condition 1IC implies

[ ]1 1( )1 ( ) ,nn a n a

n

da d ad

g b gll g d b

- - +-

é ùæ öê ú÷ç- =÷ç ÷çê úè øë û

implying

[ ]

1( )(1 )

1 1( )1 ( ) .na n nn

d add b g ad bd

a d adg ll d

b

- +- + -

- - +ì üï ïï ïé ùï ïæ öí ýê ú÷ç= - ÷ï ïç ÷çê úè øï ïë ûï ïî þ

(24)

By (23) and (24), we find

[ ]

( )

[ ]( )

1( )(1 )

1 1 11

1(1 ) 1( )(1 ) ( )(1

( ) ( )1 ( )

( ) 1 ( )

n nI n n nn n

n nn

d ad gd b g ad bd

a a d add ad

gd d ad ga

b g ad bd b g ad

l g ld l d

b

l gl

b

- +- + -

- - - +- +

æ ö - +÷ç- + ÷ç ÷ç ÷ç - + - - +è ø

ì üï ïï ïé ùï ïæ ö æ öí ýê ú÷ ÷ç ç= -÷ ÷ï ïç ç÷ ÷ç çê úè ø è øï ïë ûï ïî þ

æ ö ì üï ïï ï÷ç= -÷ í ýç ÷çè ø ï ïï ïî þ( )

) 1( )(1 ) .n

gdbdb g ad bdd

- +- + -

(25)

Then, the objective function in problem (4) becomes

[ ]

( ) ( )

( )

1 1 (1 )( )(1 ) ( )(1 ) ( )(1 )

(1 )( )(1 ) ( )(1 )

1 ( )

[1 ( )] .

n a I an

n n

ad g d ad b a bdb g ad bd b g ad bd b g ad bdg d b

b d ad bdb g ad bd b g ad bd

g g ll

b b

l d

+ - + -- + - - + - - + -

- +- + - - + -

é ùæ ö æ ö æ öê ú÷ ÷ ÷ç ç ç- - = -ê ú÷ ÷ ÷ç ç ç ÷ç÷ ÷ç ç è øê úè ø è øë û

⋅ -

(26)

Since ,g b< we have

( ) ( )1 1( )(1 ) ( )(1 )

,ad g d ad b

b g ad bd b g ad bdg gb b

+ - +- + - - + -æ ö æ ö÷ ÷ç ç>÷ ÷ç ç÷ ÷ç çè ø è ø

which guarantees a positive payoff for the EN. Then, problem (4) becomes

( )

(1 ) (1 )( )(1 ) ( )(1 ) ( )(1 )max [1 ( )] .

nn n

n

a bd b d ad bdb g ad bd b g ad bd b g ad bdl

l d

- - +- + - - + - - + -

æ ö÷ç -÷ç ÷çè ø

With ( ) ,n nl r= the above problem becomes

(1 )

( )(1 ) ( )(1 )max (1 ) .n

n nb d ad bd

b g ad bd b g ad bdr- +

- + - - + --

The first-order condition (FOC) then implies

of 48

.(1 )

n dad r

* =+

The second-order condition (SOC) is satisfied. Hence, we are sure that the solution in (6) is

correct. Then from (24), we find

( ) ( )1

( )(1 )1 1

1( )(1 )

2 1

12 ( )(1 )( )(1 )

1

11 1

11 1

a n n

d add b g ad bd

a d ad

d add b g ad bd

d ada

dd adb g ad bdb g ad bd a

gr r d

b

ad d g dr

ad b ad

ad d g dr

ad b ad

- +- + -

* * - * - +

- +- + -

- +-

- +- + -- + - -


é ùæ öê ú+ - ÷çê ú÷= ç ÷÷çê úè ø+ +ë û

æ öæ ö+ - ÷ç÷ç ÷= ÷ çç ÷÷÷ çç è ø+ +è ø.

By (25), we have

( )

( )

1 12(1 ) 1 ( )(1 )( )(1 )( )(1 )1

1 12 ( )(1( )(1 )

11 (1 )

11 1

I

gdd ad ggda b g ad bdb g ad bdb g ad bdd ad

gdd ad gb gb g ad bd a

ad d g dr

ad b ad r

ad d g dr

ad b ad

- +æ ö +÷ç- + ÷ - + -ç - + -÷ç ÷ç - + -- + è ø

- + +-- + - -

æ öæ ö+ - ÷ç÷ç ÷= ÷ çç ÷÷ çç ÷+ +è ø è ø

æ öæ ö+ - ÷ç÷ç ÷= ÷ çç ÷÷÷ çç è ø+ +è ø

),

ad bd+ -

implying

2 ( )(1 )( )(1 )1 .

1 1I

b ggb g ad bdb g ad bd aad d g d

rad b ad

-- + -- + -* -

æ öæ ö+ - ÷ç÷ç ÷= ÷ çç ÷÷÷ çç è ø+ +è ø


With a fixed ,n (24) and (25) imply

( ) ( )

( )( )

( )

1( )(1 )

1 1

1(1 ) 1 ( )(1 ) 1( )(1 )1 ( )(1 )

ˆ 1 ,

ˆ 1 ,

a n n

I n n

d add b g ad bd

a d ad

d ad ggd gda b g ad bdb g ad bdd ad b g ad bd

gr r d

b

gr r d

b

- +- + -

- - +

- +æ ö÷ç- + ÷ç - + -÷ç +÷ç - + -- + è ø - + -

ì üï ïï ï= -í ýï ïï ïî þ

ì üï ïï ï= -í ýï ïï ïî þ

which in turn imply the solution in (9).


The FOC is

of 48

( ) ( )( )

( ) ( )2

( ) ( ) ( )1 ( ) ,( )

i i ii j j j jj j j j

j j jj j jjj

n I n I n Inu x I x I x I x Ip a I I II

l l llé ù é ù¢ ¢ê ú ê ú= - +ê ú ê úê ú ê úë û ë û

å å å åå å åå

or

2

( )1 1( ) ( ) ( ) ( ) ( ) .( )

i i ii

n I I In u x I x I x I x Ip a I I I I

ll

é ù é ù¢ ¢ê ú ê ú= - +ê ú ê úë û ë û

Since we must have /iI I n= for all i in equilibrium, this FOC becomes

1 ( ) ( ) 1 ( )( ) ( ) ,( )

n x I n x In x Ip a n nI n

all

- é ùé ù ¢-ê úê ú= +ê úê úë û ë û

which implies (10).

A.5. Derivation of the Nash Investment Solution

Condition 2IC implies

( )1 11 ,na II I

ag d dr

- æ ö- ÷ç= + ÷ç ÷çè ø

implying

( )1 1 1 .I a nd ad g ar d- + -= + - (27)

By this, condition 1IC implies

( )1 1(1 ) 1 ,n a n ad

g a b gd adr g r d b- -- +é ù- + - =ë û

implying

( )1 11(1 ) 1 ,n n agdd b g

a d add adg

r r db

- -- - +- +é ù- + - =ë û

implying

( )

1( )(1 )

1 1ˆ (1 ) 1 .a n n

d add b g ad bd

a d adg

r r db

- +- + -

- - +ì üï ïï ïé ù= - + -í ýë ûï ïï ïî þ

(28)

By (27) and (28),

of 48

( ) ( )

( )

( )

( )

1( )(1 )

1 1 1 1

1( )(1 )11 ( )(1 )

1 (1 ) 1

1 (1 ) .

I n n n

n n

d ad gd b g ad bd

d ad a a d ad

d ad gdg b g ad bda b g ad bd

gr d r r d

b

gr d r

b

- +- + -

- + - - - +

- +- + -+- - + -

ì üï ïï ïé ù= + - - + -í ýë ûï ïï ïî þ

é ùé ù ê ú= + - -ë û ê úë û

(29)

Then,

( )( )(1 )1 ( )(1 )ˆ 1 (1 ) .I n n

gb g b g ad bda b g ad bd

gr d r

b

- - + -- - + -é ùé ù ê ú= + - -ë û ê úë û

Then, the objective function in problem (11) becomes

( )

( )

( )

( )

( )

1( )(1 )

1 1

( ) ( )(1 )1 ( )(1 )

1(

1 1

(1 ) (1 ) (1 ) 1

1 (1 )

(1 ) 1

n a I a n n n

n n

n n

d ad gd b g ad bd

g d b a d ad

gdb g d b g ad bda b g ad bd

d ad bd

a d ad

gr r r r d

b

gr d r

b

gr r d

b

- +- + -

- - +

- - + -- - + -

- +

- - +

ì üï ïï ïé ù- - = - - + -í ýë ûï ïï ïî þ

é ùé ù ê ú⋅ + - -ë û ê úë û

ì üï ïï ïé ù- - + -í ýë ûï ïï ïî þ( ) ( )

( )( )

( )

)(1 )

1 11( )(1 ) ( )(1 ) 1 ( )(1 )( )(1 )

,

1 1 .n n

b g ad bd

ad g d ad bbdd ad bb g ad bd b g ad bd a b g ad bdb g ad bd

g gr r d

b b

- + -

+ - +- +- + - - + - - - + -- + -

é ùæ ö æ öê ú÷ ÷ é ùç ç= - - + -ê ú÷ ÷ç ç ë û÷ ÷ç çê úè ø è øë û

(30)

Since ,g b< we have

( ) ( )1 1( )(1 ) ( )(1 )

,ad g d ad b

b g ad bd b g ad bdg gb b

+ - +- + - - + -æ ö æ ö÷ ÷ç ç>÷ ÷ç ç÷ ÷÷ ÷ç çè ø è ø

which guarantees a positive payoff for the EN. Then, problem (11) becomes

( )( )

( )1

( )(1 ) ( )(1 )max 1 1 .n

n nd ad b bd

b g ad bd b g ad bdr d- +

- + - - + -- + -

The first-order condition (FOC) is

1 ,

1 1n nd d ad

rd r

- +=

+ - -

implying

(1 )(1 ) .

(1 )n d r d ad d

ad r* + - + -

=+

The second-order condition (SOC) is satisfied. Hence, we are sure that this solution is correct.

of 48

A.6. Proof of Proposition 1

Part (a)

We have

( )( )1 0 1 .1

g db g ad bd

b ad- + - > - >

+ (31)

If 1 ,1

g db ad

- >+

then

( ) ( )2

11ˆ(1) 1 ,1 1

I Ib gg g

b ga aad d g d gr r dr

ad b ad b

--* - -

æ öæ ö é ù+ - ÷ç÷ç ÷ ê ú³ ³ -÷ çç ÷÷÷ çç è ø ê ú+ +è ø ë û

or

( ) ( )1 1 1 .b g

bgg

rr ad ad d

d

-

æ ö÷ç- + £ + -÷ç ÷çè ø (32)

Hence, if 1 ,1

g db ad

- >+

then

( ) ( )ˆ(1) 1 1 1 ;I Ib g

bgg

rr ad ad d

d

-

* æ ö÷ç³ - + £ + -÷ç ÷çè ø

and if 1 ,1

g db ad

- <+

then

( ) ( )ˆ(1) 1 1 1 .I Ib g

bgg

rr ad ad d

d

-

* æ ö÷ç£ - + £ + -÷ç ÷çè ø (33)

We also have

2

(1 ) (1 ) 0 1 .b g b b g

g g gb g gr r r r r r

r g b

- --é ù¶ -ê ú- = - - ³ £ -ë û¶

Therefore, if 1 ,gr

b£ - then

1d

rad

£+

implies

( ) ( ) ( )11 1 1 1 1 .1 1

b g b gb bg gg g

r dr ad ad ad d

d ad ad

- -

æ ö æ öæ ö÷ ÷ ÷ç ç ç- + £ - + = + -÷ ÷ ÷ç ç ç÷ç ÷ ÷ç çè ø è øè ø+ +

of 48

That is, if 1 gr

b£ - and 1 ,

1g db ad

- >+

given the c0ndition 1

dr

ad£

+ (i.e., 1),n* ³ we

have ˆ(1)I I* ³ . But, if 1 gr

b£ - and 1 ,

1g db ad

- £+

given the c0ndition ,1

dr

ad£

+ we

have ˆ(1).I I* £

On the other hand, if 1 ,gr

b³ - then

1d

rad

£+

implies

( ) ( ) ( )11 1 1 1 1 .1 1

b g b gb bg gg g

r dr ad ad ad d

d ad ad

- -

æ ö æ öæ ö÷ ÷ ÷ç ç ç- + ³ - + = + -÷ ÷ ÷ç ç ç÷ç ÷ ÷ç çè ø è øè ø+ + (34)

Given ,1

dr

ad£

+ if 1 ,g

rb

³ - then we have 1 .1

g db ad

- £+

By (33) and (34), we then

have ˆ(1).I I* ³ Part (a) is proven.

Part (b)

We have

( )( )1 0 1 .1

g db g ad bd

b ad- + - > - >

+ (35)

If 1 ,1

g db ad

- >+

then

( ) ( )1 12

11ˆ(1) 1 ,1 1

a add ad d ad

da aad d g d gr r dr

ad b ad b

- + - +* - -

æ öæ ö é ù+ - ÷ç÷ç ÷ ê ú> > -÷ çç ÷÷÷ çç è ø ê ú+ +è ø ë û

or

( ) ( )11

11 1 1 .d

add add ad

rr ad ad d

d

+- +- +

æ ö÷ç- + < + -÷ç ÷çè ø

Hence, if 1 ,1

g db ad

- >+

then

( ) ( )11

1ˆ(1) 1 1 1 ;a ad

add add ad

rr ad ad d

d

+- +* - +æ ö÷ç³ - + £ + -÷ç ÷çè ø

(36)

and if 1 ,1

g db ad

- <+

then

of 48

( ) ( )11

1ˆ(1) 1 1 1 .a ad

add add ad

rr ad ad d

d

+- +* - +æ ö÷ç³ - + ³ + -÷ç ÷çè ø

(37)

We also have

1

1 1 1(1 ) (1 ) 0 .1 1

d d dd ad d ad d add d

r r r r r rr d ad ad

-- + - + - +

é ù¶ ê ú- = - - ³ £ë û¶ - + +

The given condition is 1n* ³ or ,1

dr

ad£

+ which ensures that 1(1 )

dd adr r - +- is increasing

in .r Then, 1

dr

ad£

+ implies

( ) ( ) ( )1 11 1

1 111 1 1 1 1 .

1 1

d dad add ad d ad

d ad d adr d

r ad ad ad dd ad ad

+ +- + - +- + - +

æ ö æ öæ ö÷ ÷ ÷ç ç ç- + £ - + = + -÷ ÷ ÷ç ç ç÷ç ÷ ÷ç çè ø è øè ø+ +

Hence, if 1 ,1

g db ad

- >+

by (36), we have ˆ(1);a a* ³ and if 1 ,1

g db ad

- <+

by (37), we

have ˆ(1).a a* £ Part (b) is proven.

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Tables

Table 1. The Sample Distribution

The sample consisted of 40,395 VC investment rounds led by 2,373 lead VCs and made in 15,264 portfolio companies that received their initial VC funding during

1985–2005 and for which there were relevant data in the database. The table presents the distribution of VC investment rounds by funding year and the industry,

location and development stage of the portfolio company. The number of observations and the corresponding percentages are listed.

Year Obs. Percent Industry Obs. Percent Location Obs. Percent Stage Obs. Percent

1985 456 1.13 Agriculture/Forestry/Fishing 70 0.17 California 14863 36.79 Seed Stage 5500 13.62

1986 732 1.81 Biotechnology 2776 6.87 Massachusetts 4605 11.40 Early Stage 10651 26.37

1987 1056 2.61 Business Services 773 1.91 Texas 2358 5.84 Expansion Stage 18025 44.62

1988 1122 2.78 Communications 4565 11.30 New York 1823 4.51 Later Stage 6219 15.40

1989 1211 3.00 Computer Hardware 1901 4.71 Pennsylvania 1335 3.30 Total 40395 100

1990 1227 3.04 Computer Other 105 0.26 Washington 1224 3.03

1991 1030 2.55 Computer Software 9280 22.97 Colorado 1203 2.98

1992 1081 2.68 Construction 98 0.24 New Jersey 1184 2.93

1993 936 2.32 Consumer Related 2252 5.57 Georgia 1059 2.62

1994 886 2.19 Financial Services 630 1.56 Virginia 1057 2.62

1995 1206 2.99 Industrial/Energy 1650 4.08 Illinois 943 2.33

1996 1664 4.12 Internet Specific 7396 18.31 Maryland 901 2.23

1997 2153 5.33 Manufacturing 422 1.04 North Carolina 818 2.03

1998 2690 6.66 Medical/Health 5193 12.86 Minnesota 808 2.00

1999 3966 9.82 Semiconductor/Electronics 2929 7.25 Florida 805 1.99

2000 5061 12.53 Transportation 288 0.71 Connecticut 758 1.88

2001 3576 8.85 Utilities 26 0.06 Ohio 591 1.46

2002 2593 6.42 Other 41 0.10 Oregon 401 0.99

2003 2465 6.10 Total 40395 100 Tennessee 400 0.99

2004 2619 6.48 Arizona 345 0.85

2005 2665 6.60 other 2914 7.21

Total 40395 100 Total 40395 100

of 48

Table 2. Variable Definitions, Measures and Data Sources

The table presents definitions and measures for the dependent, independent and control variables. Dummy

variables are indicated by *. Variables used as the natural logarithm are indicated by **.

Variables Definition and Measurement

Dependent Variables

Syndicate Size** The logarithm of the number of VCs participating in an investment round.

Network Degree The normalized number of VCs that a lead VC had syndicated with in the 5 years prior to the current investment round.

Network Outdegree The normalized number of VCs that a lead VC had invited into her syndicates in the 5 years prior to the current investment round.

Network Indegree The normalized number of VCs that a lead VC had been invited into their syndicates in the 5 years prior to the current investment round.

Investment Risk:

Company Age** The logarithm of the age of a portfolio company at the current investment round. The age of a portfolio company is the number of years between its founding and the year of the current investment round.

Industry Distance (%) The proportion of investment rounds made previously by a lead VC that were not made in the given portfolio company’s industry.

Stage Distance (%) The proportion of investment rounds made previously by a lead VC that were not made in the same development stage as the given portfolio company.

Geographic Distance** The logarithm of the geographic distance (in kilometers) between the resident state of a portfolio company and its lead VC.

Portfolio Company Quality:

Total VC Funding** The logarithm of one plus the total VC funding across all financing rounds.

Quality Indicator* A dummy variable indicating whether the VC-backed portfolio company went public or was acquired before the end of 2009.

Lead VC Type:

Corporate VC Indicator* A dummy variable indicating whether a lead VC firm was affiliated with a corporation.

Institutional VC Indicator* A dummy variable indicating whether a lead VC firm was affiliated with an institution.

Government VC Indicator* A dummy variable indicating whether a lead VC firm was affiliated with a government.

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Table 3. Summary Statistics of VC Investment Rounds

The table presents summary statistics describing 40,395 VC investment rounds made in those portfolio

companies that received initial VC funding during 1985–2005 and for which there were relevant data in the

database. The definitions, measures and data sources of the variables are described in Table 2. The quartiles,

means, standard deviations and the number of observations are presented.

Obs. Mean Std. 0.25 0.5 0.75

Dependent Variables:

Syndicate Size 40,395 2.37 1.89 1 2 3

Network Degree (%) 40,395 6.91 7.48 1.23 4.39 9.82

Network Outdegree (%) 40,395 3.02 4.71 0.22 1.16 3.62

Network Indegree (%) 40,395 1.34 1.37 0.25 0.90 2.08

Investment Risk:

Company Age (years) 40,395 4.79 8.43 1 3 5

Industry Distance (%) 40,395 79.85 20.53 73.01 85.17 94.25

Stage Distance (%) 40,395 67.54 20.55 54.44 70 81.90

Geographic Distance (km) 40,395 1207.95 1457.47 0 363.9 2505.9


Total VC Funding ($mil) 40,395 31.08 40.24 6.44 18.11 41.22

Quality Indicator 40,395 0.38 0.48

Lead VC Type:

Corporate VC Indicator 40,395 0.03 0.17

Institutional VC Indicator 40,395 0.04 0.20

Government VC Indicator 40,395 0.11 0.31

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Table 4. Correlation Matrix

The table presents the Spearman and Pearson correlation matrices among all the variables respectively in the upper and lower diagonals. The sample consisted of

40,395 VC investment rounds made in those portfolio companies that received initial VC funding during 1985–2005 and for which there were relevant data in the

database. The definitions, measures and data sources of the variables are described in Table 2. The significance level at 5% is indicated by *.

1 2 3 4 5 6 7 8 9 10 11 12 13

Dependent Variables:

1 Syndicate Size 0.23* 0.29* 0.15* -0.03* -0.05* 0.01 0.07* 0.41* 0.14* -0.01 0.01 -0.06*

2 Network Degree 0.20* 0.88* 0.90* -0.04* -0.04* -0.02* 0.10* 0.14* 0.14* -0.11* 0.03* -0.14*

3 Network Outdegree 0.24* 0.86* 0.71* -0.01* -0.04* -0.05* 0.12* 0.23* 0.13* -0.13* -0.003 -0.15*

4 Network Indegree 0.12* 0.86* 0.58* -0.05* -0.06* -0.004 0.05* 0.12* 0.12* -0.11* -0.002 -0.13*

Investment Risk:

5 Company Age -0.03* -0.06* -0.03* -0.06* -0.04* -0.13* 0.08* -0.03* 0.01* -0.003 0.05* 0.01

6 Industry Distance 0.002 0.16* 0.14* 0.13* 0.002 0.15* 0.001 -0.10* -0.02* -0.04* 0.04* 0.04*

7 Stage Distance 0.02* 0.06* 0.04* 0.06* -0.14* 0.120* -0.05* -0.01 0.03* -0.002 -0.02* -0.004

8 Geographic Distance 0.05* 0.08* 0.11* 0.03* 0.10* 0.002 -0.04* 0.09* 0.02* 0.04* 0.08* -0.06*


9 Total VC Funding 0.37* 0.08* 0.11* 0.09* -0.08* -0.07* -0.03* 0.06* 0.16* 0.04* -0.02* -0.12*

10 Quality Indicator 0.15* 0.14* 0.12* 0.11* 0.003 -0.001 0.02* 0.004 0.16* 0.007 -0.003 -0.06*

Lead VC Type:

11 Corporate VC Indicator -0.004 -0.09* -0.09* -0.06* -0.007 -0.08* 0.004 0.04* 0.02* 0.01* -0.07* -0.04*

12 Institutional VC Indicator 0.02* 0.07* 0.05* 0.06* 0.067* 0.03* -0.02* 0.10* -0.04* -0.003 -0.07* -0.06*

13 Government VC Indicator -0.06* -0.11* -0.09* -0.11* 0.01* 0.02* 0.01* -0.06* -0.14* -0.06* -0.04* -0.06*

of 48

Table 5. Regression Results

The sample consisted of 40,395 VC investment rounds made in those portfolio companies that received initial

VC funding during 1995–2005 and for which there were relevant data in the databases. The table presents OLS

regression results relating the dependent variable (Syndication Size, Network Degree, Network Outdegree or

Network Indegree) to the factors including investment risk and portfolio company quality as well as other control

variables. The definitions, measures and data sources of the variables are described in Table 2. Funding year,

industry and round sequence fixed effects were included in all the regressions (not reported). Intercepts are not

reported. Robust t-values are in parentheses. The significance levels at 1%, 5% and 10% are identified by ***, ** and

*, respectively.

Syndicate Size Network Degree

Network Outdegree

Network Indegree

Expected Sign

1 2 3 4 5

Investment Risk:

Company Age - -0.064 -0.022 -0.582 -0.275 -0.108

(-17.40)*** (-6.00)*** (-13.60)*** (-10.05)*** (-12.66)***

Industry Distance + 0.002 0.002 0.053 0.031 0.009

(11.32)*** (10.65)*** (44.39)*** (43.49)*** (37.64)***

Stage Distance 0.001 0.001 0.006 0.002 0.002

(5.54)*** (4.68)*** (4.07)*** (2.88)*** (5.33)***

Geographic Distance + 0.009 0.006 0.102 0.115 0.004

(10.73)*** (6.97)*** (12.00)*** (20.29)*** (2.37)**


Total VC Funding + 0.11 0.599 0.354 0.083

(54.89)*** (27.61)*** (27.56)*** (19.54)***

Quality Indicator + 0.126 0.684 0.468 0.085

(19.13)*** (9.94)*** (9.90)*** (6.26)***

Lead VC Type:

Corporate VC Indicator +/- -0.046 -0.039 -2.032 -1.637 -0.253

(-2.75)*** (-2.35)** (-12.67)*** (-26.3)*** (-5.91)***

Institutional VC Indica-tor

+/- 0.057 0.061 1.174 0.393 0.232

(5.48)*** (6.03)*** (9.03)*** (4.29)*** (8.04)***

Government VC Indica-tor

+/- -0.16 -0.023 -2.819 -1.411 -0.554

(-9.89)*** (-1.41) (-25.42)*** (-23.93)*** (-23.55)***

Year, industry and round sequence fixed effects

Present Present Present Present Present

No. of Observations 40,395 40,395 40,395 40,395 40,395

R2 0.115 0.197 0.295 0.178 0.172

endogenous networks in investment syndication

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